Week 13 Discussion — How Sure Is Sure Enough?
Hook
A student says they guessed on every question of a 10-question quiz with four options per question, and they scored 7. This week you tested that claim. If the student were purely guessing, a score of 7 or more would occur on about 35 quizzes in 10,000, a p-value of 0.0035, so at a significance level of α = 0.05 you reject H₀. That arithmetic is the easy part. Every test also carries two judgments that no formula makes for you: how much risk of a false alarm you will accept, and whether a "significant" result is big enough to matter.
Your driving question — choose Option A or Option B; they carry the same weight and the same rubric, and you say which you picked.
Option A: Pick a real yes-or-no decision made under uncertainty in your life, your major, your job, or your community, such as a smoke alarm, a medical screening test, a spam filter, a safety check on a product, or a jury verdict. Say what the null hypothesis would be there, and what a Type I error and a Type II error would each look like. Then argue which of the two errors is worse in that setting, and whether you would set the significance level at 0.05, stricter, or looser. Use the guessing quiz as your reference: the rule "reject when the score is 5 or more" wrongly flags a pure guesser with probability 0.0781, the stricter rule "7 or more" does so with probability 0.0035, and the stricter rule misses more students who really do know some of the material.
Option B: Take a position on this claim: "If a study's p-value is below 0.05, its result matters and people should act on it." Start from the guessing quiz: a score of 4 out of 10 (40%) has a p-value of 0.2241, while a score of 40 out of 100 on a 100-question version, the same 40%, sits about 3.46 standard deviations above the guessing mean of 25 and has a p-value well below 0.01. Then bring in a setting from your major or your work, such as a new study method, a medicine, a change to a store's prices, or a training program, and argue when a small p-value should and should not change a real decision. Along the way, say in your own words what a p-value does and does not tell you.
There is no single right answer. A smoke alarm, a cancer screening, and a jury can each be argued well in more than one direction, and reasonable people weigh a modest but real edge differently in medicine, business, and education.
Expectations
Activity format: a multi-exchange dialogue or an equivalent structured written exchange, followed by one discussion-board post. Plan on about 45 minutes for either route, and post by the due date your instructor sets in Canvas.
There are two ways to complete this discussion. They are worth the same 10 points and scored by the same rubric. Pick either one.
Route A — the AI dialogue (the default). Hold a real conversation about the driving question with your own chatbot, then post what it produces:
- Open any approved chatbot in a new conversation.
- Copy the entire prompt box below and paste it as your first message.
- Have the conversation. It will ask you questions and push back; it will not write your post for you and will not stop after one word from you.
- Post the chatbot's summary report plus the conversation's share link to the Week 13 discussion board. That post is your entire submission. You may post the summary as text, or record it as audio or video with a transcript attached; both forms are scored by the same rubric.
No replies to classmates are required.
Route B — the written route. See Equivalent route (no AI required) below.
Integrity note. Whichever route you take, the thinking and the words you post are your own. Bring a real decision or a real study claim from your own life, work, or community; do not ask a chatbot to invent one for you, and do not let it supply numbers you cannot trace to a source.
Discussion Partner Prompt
ROLE: You are my discussion partner for an introductory statistics course. Your
job is to draw out and challenge MY thinking about the question below. You will
never write my post for me and never hand me an answer - you ask questions that
make me reason it through.
THE QUESTION I AM EXPLORING (two options of equal weight - ask which one I choose first):
Option A: Pick a real yes-or-no decision made under uncertainty in your life,
your major, your job, or your community, such as a smoke alarm, a medical
screening test, a spam filter, a safety check on a product, or a jury verdict.
Say what the null hypothesis would be there, and what a Type I error and a Type
II error would each look like. Then argue which of the two errors is worse in
that setting, and whether you would set the significance level at 0.05,
stricter, or looser. Use the guessing quiz as your reference: the rule "reject
when the score is 5 or more" wrongly flags a pure guesser with probability
0.0781, the stricter rule "7 or more" does so with probability 0.0035, and the
stricter rule misses more students who really do know some of the material.
Option B: Take a position on this claim: "If a study's p-value is below 0.05,
its result matters and people should act on it." Start from the guessing quiz:
a score of 4 out of 10 (40%) has a p-value of 0.2241, while a score of 40 out of
100 on a 100-question version, the same 40%, sits about 3.46 standard deviations
above the guessing mean of 25 and has a p-value well below 0.01. Then bring in a
setting from your major or your work, such as a new study method, a medicine, a
change to a store's prices, or a training program, and argue when a small
p-value should and should not change a real decision. Along the way, say in
your own words what a p-value does and does not tell you.
REFLECTION TARGETS (steer toward these; never read this list aloud to me):
- whether I state the null hypothesis H0 as the "nothing is going on" claim
about a parameter or a situation, and the alternative Ha as what I look for
evidence of
- whether I match a Type I error (rejecting an H0 that is true, a false alarm)
and a Type II error (failing to reject an H0 that is false, a miss) to the
right outcomes in my own setting
- whether I see that a stricter significance level (a smaller alpha) cuts Type I
errors but raises beta, the chance of a Type II error, so choosing alpha is a
trade-off and not a free improvement
- whether I describe a p-value as how surprising the data would be if H0 were
true, and not as the probability that H0 is true, the chance the result is a
fluke, or the size of the effect
- whether I keep statistical significance apart from practical significance,
and say "fail to reject H0" rather than "accept H0"
DIALOGUE RULES: greet me warmly and ask my first name before your first content
question. If I decline or give no name, call me "there" and continue without
pressure. If you still do not know my name when the summary is due, ask once more;
if I decline again, use "Discussion participant." Never invent a name. Ask ONE
question per message, then wait. Build on my exact words without praising agreement
or calling every answer "great." Probe unsupported claims and introduce the
strongest fair counterpoint. Praise only a specific, earned move I actually made,
such as revising a claim or answering the counterpoint. Never accept a one-word
answer - ask again, differently. Never lecture, and never supply a number or a
study result for me. Every message you send before the summary ends with a
question.
EXIT CONDITION: continue until this exact boolean is true — at least five substantive exchanges AND the student has stated a position AND provided at least one reason OR example AND engaged with one fair counterpoint, stopping only after whichever threshold happens LAST. A reason alone or an example alone can satisfy the support branch; do not require both, and do not require that I "answered" the counterpoint. A greeting, my name, or a one-word answer is not a substantive exchange.
THEN produce a summary report using exactly these eight labelled fields in this
order, drawn only from what I actually said. If I never supplied a field, write
"Not supplied" rather than inventing it:
1. STUDENT NAME
2. POSITION
3. REASON
4. EXAMPLE
5. COURSE CONCEPTS
6. COUNTERPOINT
7. RESPONSE TO THE COUNTERPOINT
8. OPEN QUESTION OR NEXT CHECK
Do not mention an initial post or replies to peers or classmates.
REQUIRED CLOSING — perform these final two instructions exactly:
Then say, verbatim: "Copy this summary AND your share link to this chat, and post both to the Week 13 discussion board — that completes the assignment."
Then END with one genuine earned-praise sentence that names a real move the student made.
Equivalent route (no AI required)
You never have to create an account with a chatbot company to earn full credit in this course. This route assesses the same objectives as the AI dialogue — carrying out and interpreting a hypothesis test, including what a p-value means, how a significance level and the two error types trade off, and why statistical significance is not practical significance, with the guessing quiz's binomial probabilities as the reference — against the same driving question and the same rubric below, for the same 10 points. Choosing it costs you nothing, and you do not have to tell me why you chose it.
What you do. Write a structured written exchange with yourself — the same back-and-forth the dialogue would have produced, on paper:
- Your position (roughly 150 words). Answer Option A or Option B. Describe your real decision or study claim, give your position with a reason, and use this week's terms (null hypothesis, alternative hypothesis, test statistic, p-value, significance level, Type I error, Type II error, power, statistically significant, practical significance) correctly.
- The strongest objection (roughly 100 words). Write the best argument against your own position that you can — for example, that a false alarm wastes so much time and trust that it is the worse error after all, that a stricter α lets too many real problems slip through, or that a tiny p-value is reason enough to act whatever the size of the effect. Argue it honestly; a weak objection you knock over earns no credit.
- Your response to it (roughly 100 words). Take that objection seriously. You may concede part of it — saying what would change your mind is worth more than defending everything.
- One thing you would still check (one or two sentences). What detail about the setting, the cost of each error, or the size of the effect would settle it?
Effort. Roughly 350–400 words of your own writing, comparable to the time the AI dialogue takes — about forty-five minutes including the thinking.
What you submit. Post those four parts, under those four labels, as your Week 13 discussion post. That post is your entire submission; this route has no share link.
No replies to classmates are required.
Participation rubric
This discussion is worth 10 points. The same three criteria score both routes.
| Criterion | Full credit | Partial credit | No credit |
|---|---|---|---|
| Depth of reasoning shown (4 pts) | A real, specific decision or study claim is described, and the position is supported with a reason tied to the cost of each error, the size of an effect, or a real decision someone would make | A setting is present, but the position is asserted without a reason, or the two errors are named without weighing them | Missing, off-topic, or no reasoning about the test |
| Genuine engagement with a counterpoint (3 pts) | A real objection is stated at its strongest, such as "a false alarm is the worse error here" or "a tiny p-value is reason enough to act", and then met or partly conceded | An objection is named but brushed aside, or met without engaging it | No counterpoint appears |
| Use of the week's course concepts (3 pts) | Uses this week's terms precisely, matches each error type to the right outcome, reads a p-value as computed assuming H₀ is true, and says "fail to reject" rather than "accept" | Uses a term loosely or with a small error | No course terms, or used incorrectly |
Built with The Course Maker · samples.thecoursemaker.com